# 3.2.2 Specific Heat Capacity

### Specific Heat Capacity

• If the temperature of the system increases, the increase in temperature of this system depends on:
• The mass of the substance heated
• The type of material
• The energy input to the system
• The energy input is in the form of thermal energy
• The amount of thermal energy needed to raise the temperature of a given mass by a given amount can be calculated using the equation:

ΔE = mcΔθ

• Where:
• ΔE = change in thermal energy, in joules (J)
• m = mass, in kilograms (kg)
• c = specific heat capacity, in joules per kilogram per degree Celsius (J/kg °C)
• Δθ = change in temperature, in degrees Celsius (°C)
• The specific heat capacity, c of a substance is defined as:

The amount of energy required to raise the temperature of 1 kg of the substance by 1 °C

• Different substances have different specific heat capacities
• If a substance has a low specific heat capacity, it heats up and cools down quickly (ie. it takes less energy to change its temperature)
• If a substance has a high specific heat capacity, it heats up and cools down slowly (ie. it takes more energy to change its temperature)

Low v high specific heat capacity

• Specific heat capacity is mainly used for liquids and solids
• The specific heat capacity of different substances determines how useful they would be for a specific purpose eg. choosing the best material for kitchen appliances
• Good electrical conductors, such as copper and lead, are excellent conductors of heat due to their low specific heat capacity
• On the other hand, water has a very high specific heat capacity, making it ideal for heating homes as the water remains hot in a radiator for a long time
• The specific heat capacity of some substances are given in the table below as examples:

Table of values of specific heat capacity for various substances

#### Worked Example

Water of mass 0.48 kg is increased in temperature by 0.7 °C. The specific heat capacity of water is 4200 J / kg °C.

Calculate the amount of energy transferred to the water.

Step 1: Write down the known quantities

• Mass, m = 0.48 kg
• Change in temperature, Δθ = 0.7 °C
• Specific heat capacity, c = 4200 J / kg °C

Step 2: Write down the relevant equation

ΔE = mcΔθ

Step 3: Calculate the energy transferred by substituting in the values

ΔE = (0.48) × (4200) × (0.7) = 1411.2

Step 4: Round the answer to 2 significant figures

ΔE = 1400 J

#### Exam Tip

This equation will be given on your equation sheet, so don’t worry if you cannot remember it, but it is important that you understand how to use it. You will always be given the specific heat capacity of a substance, so you do not need to memorise any values.

### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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